ASUPRA COMPACITĂŢII UNOR OPERATORI INTEGRALI SINGULARI

Abstract

The operators such as
aP  PaI , aQ QaI
and integral operators with weak
singularities are studied in the work. It is proven that the operators
aP  PaI
and
aQ QaI
are totally
continuous (or compact) in spaces with weights in one and only one case, when the function
a(t)
is
continuous on the contour of integration. As a corollary, it is shown that the factor-algebra generated by
singular operators with piecewise continuous coefficients is not comutative and the symbol on that algebra
is a matrix-function.